BRUSSELS (Reuters) - Britain said on Tuesday it had asked the European Union to put the military wing of Islamist group Hezbollah on its list of terrorist organizations.

Britain's request came after Bulgaria accused the Lebanese militant movement on February 5 of carrying out a bomb attack on a bus in the Black Sea city of Burgas that killed five Israelis and their Bulgarian driver in July last year.

"We firmly believe that an appropriate EU response (to the Burgas bombing) would be to designate Hezbollah's military wing as a terrorist organization," a spokesman for the British Foreign Office said.

There is growing concern in the West about Iranian-backed Hezbollah's involvement in the Syrian conflict.

About 30 Hezbollah fighters were killed on Sunday, Syrian activists said, along with 20 Syrian troops and militiamen loyal to President Bashar al-Assad during fierce fighting in the rebel stronghold of Qusair, near the Lebanese border.

Britain's request will be discussed in early June in a special EU working group. Many European governments are cautious about imposing sanctions on Hezbollah, arguing it could fuel tensions in the Middle East. European governments and companies must cease any financial dealings with groups on the list.

(Reporting by Adrian Croft; Editing by Rex Merrifield and Pravin Char)